Residual-Based Tests for Fractional Cointegration: Testing the Term Structure of Interest Rates

Campbell and Shiller (1987) and Hall et al. (1992) suggest that the term spread of long-term and short-term interest rates should be a stationary I(0) process. However, an empirically nonstationary term spread or rejection of cointegration between long and short term interest rates need not to be considered an empirical rejection of this theoretical relationship. It is likely that the dichotomy between I(1) or I(0) and/or integer values of cointegration are environments which are too restrictive to model the term structure. To overcome this problem, we propose a residual-based approach to test for the null of no cointegration against a fractional alternative which relies on the Exact Local Whittle Estimator (Shimotsu and Philllips, 2005, 2006). We compare its performance to other residual-based tests for fractional cointegration, and then we use it to investigate the term structure in the U.K and the U.S.